Meson Production in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>d</mml:mi></mml:math>Collisions and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mn/></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mo>−</mml:mo><mml:mi>π</mml:mi></mml:math>Interaction. IV. Double-Pion Production and Pion-Pion Scattering

We present an analysis of the measurements on the reaction $p+d\ensuremath{\rightarrow}{\mathrm{He}}^{3}+2\ensuremath{\pi}$, and show that the anomalous bump in the ${\mathrm{He}}^{3}$ spectrum cannot be accounted for by $\ensuremath{\pi}$-${\mathrm{He}}^{3}$ final-state interactions, by Bose statistics for the two pions, or by the deuteron and ${\mathrm{He}}^{3}$ wave functions. However, the anomaly can be satisfactorily explained by a strong final-state interaction between the two pions. We determine the $S$-wave $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering length in the $I=0$ state to be 2\ensuremath{\Elzxh}/\ensuremath{\mu}c.